Algebra Examples

$\frac{3}{5} (3 x - 1) > 12$

Step 1

Solve $x > 7$ .

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Step 1.1

Simplify $\frac{3}{5} (3 x - 1)$ .

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Step 1.1.1

Apply the distributive property.

$\frac{3}{5} (3 x) + \frac{3}{5} \cdot - 1 > 12$

Step 1.1.2

Multiply $\frac{3}{5} (3 x)$ .

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Step 1.1.2.1

Combine $3$ and $\frac{3}{5}$ .

$\frac{3 \cdot 3}{5} x + \frac{3}{5} \cdot - 1 > 12$

Step 1.1.2.2

Multiply $3$ by $3$ .

$\frac{9}{5} x + \frac{3}{5} \cdot - 1 > 12$

Step 1.1.2.3

Combine $\frac{9}{5}$ and $x$ .

$\frac{9 x}{5} + \frac{3}{5} \cdot - 1 > 12$

Step 1.1.3

Multiply $\frac{3}{5} \cdot - 1$ .

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Step 1.1.3.1

Combine $\frac{3}{5}$ and $- 1$ .

$\frac{9 x}{5} + \frac{3 \cdot - 1}{5} > 12$

Step 1.1.3.2

Multiply $3$ by $- 1$ .

$\frac{9 x}{5} + \frac{- 3}{5} > 12$

Step 1.1.4

Move the negative in front of the fraction.

$\frac{9 x}{5} - \frac{3}{5} > 12$

Step 1.2

Move all terms not containing $x$ to the right side of the inequality.

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Step 1.2.1

Add $\frac{3}{5}$ to both sides of the inequality.

$\frac{9 x}{5} > 12 + \frac{3}{5}$

Step 1.2.2

To write $12$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9 x}{5} > 12 \cdot \frac{5}{5} + \frac{3}{5}$

Step 1.2.3

Combine $12$ and $\frac{5}{5}$ .

$\frac{9 x}{5} > \frac{12 \cdot 5}{5} + \frac{3}{5}$

Step 1.2.4

Combine the numerators over the common denominator.

$\frac{9 x}{5} > \frac{12 \cdot 5 + 3}{5}$

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $12$ by $5$ .

$\frac{9 x}{5} > \frac{60 + 3}{5}$

Step 1.2.5.2

Add $60$ and $3$ .

$\frac{9 x}{5} > \frac{63}{5}$

Step 1.3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$9 x > 63$

Step 1.4

Divide each term in $9 x > 63$ by $9$ and simplify.

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Step 1.4.1

Divide each term in $9 x > 63$ by $9$ .

$\frac{9 x}{9} > \frac{63}{9}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $9$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{9 x}{9} > \frac{63}{9}$

Step 1.4.2.1.2

Divide $x$ by $1$ .

$x > \frac{63}{9}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Divide $63$ by $9$ .

$x > 7$

Step 2

Use the inequality $x > 7$ to build the set notation.

${x | x > 7}$

Step 3